Calculations in the Generalized Lubin–Tate Theory

Результат исследований: Научные публикации в периодических изданияхстатьярецензирование

Аннотация

Abstract: In this paper, various extensions of local fields are considered. For arbitrary finite extension K of the field of p-adic numbers, the maximum Abelian extension KAb/K and the corresponding Galois group can be described using the well-known Lubin–Tate theory. It is represented as a direct product of groups obtained using the maximum unramified extension of K and a fully ramified extension obtained using the roots of some endomorphisms of Lubin–Tate formal groups. We consider the so-called “generalized Lubin–Tate formal groups” and extensions obtained by adding the roots of their endomorphisms to the field under consideration. Using the fact that a correctly chosen generalized formal group coincides with the classical one over unramified finite extension Tm of degree m of field K, it was possible to obtain the Galois group of the extension (Tm)Ab/K. The main result of the work, is an explicit description of the Galois group of the extension (Kur)Ab/K, where Kur is the maximum unramified extension of K. Similar methods are also used to study ramified extensions of the field K.

Язык оригиналаанглийский
Страницы (с-по)131-135
Число страниц5
ЖурналVestnik St. Petersburg University: Mathematics
Том53
Номер выпуска2
DOI
СостояниеОпубликовано - 1 апр 2020

Предметные области Scopus

  • Математика (все)

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